What Is the Radius of the n = 6 Bohr Orbit in O7+?

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Homework Help Overview

The problem involves calculating the radius of the n = 6 Bohr orbit for the O7+ ion, which is an oxygen atom with 7 of its 8 electrons removed. The discussion centers around the application of the Bohr model and the relevant equations for hydrogen-like ions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the appropriate formula for calculating the radius, noting the need to consider the nuclear charge (Z) for oxygen. There is a question about the specific equation that incorporates Z, as the original poster's formula appears to be incomplete for this context.

Discussion Status

Some participants have provided guidance regarding the need to adjust the formula for the nuclear charge, while others are seeking the correct equation that accounts for this factor. The discussion is ongoing, with multiple interpretations being explored.

Contextual Notes

The original poster expresses confusion over the correct application of the formula and the expected answer, indicating a potential gap in understanding the adjustments needed for ions with higher nuclear charges.

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Homework Statement


Calculate the radius of the n = 6 Bohr orbit in O7+(oxygen with 7 of its 8 electrons removed).
A) 190 pm B) 167 pm C) 238 pm D) 214 pm


Homework Equations



I believe that the relevant equation is
r(sub n)=(n^2)*a(sub b) where a(sub b)= Bohr's radius= 5.29*10^-11 m

The Attempt at a Solution


I calculated it for what I believed to be n=6, but I got an incorrect answer. The correct answer is (C) 238 pm, but I do not understand why.


Any help is greatly appreciated!
 
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Your formula is not quite complete. You need to take into account the charge in the nucleus (so the number of protons).
 
Welcome to PF :smile:

Your equation is for hydrogen, with a charge of +1 on the nucleus.
Since oxygen has a charge of Z=8 for the nucleus, that equation should be different, containing Z somehow.

Does your textbook discuss "hydrogen-like" or "hydrogenic" ions?

EDIT: ah, I should know better than to wait a 1/2 hour and then respond without refreshing the page. :redface:
 
Unfortunately,
I cannot find an equation that takes into account (Z). Anyone have the equation handy?
Thanks for all your help!
 
Thank you very much!
 

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